Quaternion

A quaternion is a number of the form a+bi+cj+dk with real coefficients and noncommutative multiplication. Quaternions form a four-dimensional associative division algebra over the real numbers.

Real number: A number on the continuous one-dimensional number line, including rational and irrational values. Each quaternion coefficient is real.
Quaternion conjugate: The quaternion a+bi+cj+dk mapped to a−bi−cj−dk. Conjugation reverses the signs of the three imaginary components.
Rotation representation: A mathematical encoding of spatial rotations using coordinates or algebraic objects. Unit quaternions encode rotations without the singularities of some coordinate systems.
William Rowan Hamilton: An Irish mathematician who introduced quaternions in 1843. Hamilton developed the algebra after seeking a three-dimensional analogue of complex numbers.
Complex number: A number of the form a+bi, where a and b are real and i²=−1. Quaternions extend complex numbers with two additional imaginary units.
Quaternion norm: The nonnegative real number √(a²+b²+c²+d²) associated with a quaternion. The norm converts quaternion magnitude into a real scalar.
Unit quaternion: A quaternion whose norm is one. Unit quaternions represent rotations while preserving vector lengths.
On Quaternions: William Rowan Hamilton's 1853 book presenting the theory and applications of quaternions. The book established quaternion algebra as a systematic mathematical subject.
Quaternion unit: One of the basis elements 1, i, j, and k used to express a quaternion. These four units define the coordinates and multiplication rules.
Quaternion inverse: For nonzero q, the quaternion q⁻¹=q*/|q|², where q* is its conjugate. The conjugate and norm together produce the multiplicative inverse.

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